Study of final-state interactions of protons in neutrino-nucleus scattering with INCL and NuWro cascade models

The modeling of neutrino-nucleus interactions constitutes a challenging source of systematic uncertainty for the extraction of precise values of neutrino oscillation parameters in long-baseline accelerator neutrino experiments. To improve such modeling and minimize the corresponding uncertainties, a new generation of detectors is being developed, which aim to measure the complete final state of particles resulting from neutrino interactions. In order to fully benefit from the improved detector capabilities, precise simulations of the nuclear effects on the final-state nucleons are needed. This article presents the study of the in-medium propagation of knocked-out protons, i.e., final-state interactions (FSI), comparing the NuWro and INCL cascade models. The INCL model is used here for the first time to predict exclusive final states in measured neutrino interaction cross sections. This study of INCL in the framework of neutrino interactions features various novelties, including the production of nuclear clusters (e.g., deuterons, $\alpha$ particles) in the final state. The paper includes a complete characterization of the final state after FSI, comparisons to available measurements of single transverse variables, and an assessment of the observability of nuclear clusters.

Figure 1

Cross section of proton-${}^{12}\mathrm{C}$ interactions as a function of the proton momentum: comparison of the INCL and NuWro models to available experimental data [66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84]. Results of the NuWro 19.02.2 simulation are taken from Ref. [65].

Figure 2

Momentum distribution of neutrons in the nucleus for NuWro SF and RFG and INCL nuclear models (comparison of the shapes between unit-normalized distributions).

Figure 3

Radial coordinate and momentum distribution inside the nucleus for INCL (top) and NuWro LFG (bottom) nuclear models ($z$ axis in arbitrary units).

Figure 4

Position distribution of neutrons in INCL and NuWro and of the INCL neutron chosen to match the SF neutron simulated in NuWro in our matching algorithm.

Figure 5

STV representation in the plane perpendicular to the neutrino direction.

Figure 6

Scheme of the particle simulation and identification algorithm in a segmented scintillating detector. The shaded line indicates the cluster track traversing multiple scintillating cubes. The cluster has initial kinetic energy $E^0$ and deposits energy $E_i^{\mathrm{dep}}$ in each cube. The last cube, where the cluster stops, is not considered in the identification algorithm.

Figure 7

Nuclear transparency of ${}^{12}\mathrm{C}$ (percentage of events without FSI) as a function of proton momentum modeled by NuWro and INCL.

Figure 8

Top: proton momentum before FSI for INCL (left) and NuWro (right) cascade models in CCQE events with T2K neutrino energy flux. Subprocesses correspond to the fate of the proton after FSI. The shape of the proton momentum before FSI is by definition identical for INCL and NuWro cascades. Bottom: leading proton momentum after FSI for INCL (left) and NuWro SF (right) nuclear models. The fractions of different FSI subprocesses as listed in Table 1 is also shown. The zero-proton channel in NuWro includes events with only a muon in the final state, as well as pion, and neutron production channels. There is no cluster production in NuWro.

Figure 9

Distribution of the leading proton’s momentum in NuWro SF and $\mathrm{NuWro}+\mathrm{INCL}$ before and after FSI (top left, comparison of the shapes between unit-normalized distributions), the difference in the proton’s momentum before and after FSI ($\mathrm{\Delta }P=P_{\text{after}}-P_{\text{before}}$) in NuWro SF and $\mathrm{NuWro}+\mathrm{INCL}$ (bottom left, comparison of the shapes between unit-normalized distributions), the leading proton $\cos (\mathrm{\Theta }$) in NuWro SF and $\mathrm{NuWro}+\mathrm{INCL}$ before and after FSI (top right, comparison of the shapes between unit-normalized distributions), and the difference in the proton’s $\cos (\mathrm{\Theta }$) before and after FSI ($\mathrm{\Delta }\cos \mathrm{\Theta }=\cos {\mathrm{\Theta }}_{\text{after}}-\cos {\mathrm{\Theta }}_{\text{before}}$) in NuWro SF and $\mathrm{NuWro}+\mathrm{INCL}$ (bottom left, comparison of the shapes between unit-normalized distributions). The “no FSI” channel is excluded. CCQE events with T2K neutrino energy flux are simulated.

Figure 10

Top: $\delta {\mathrm{p}}_T$ distribution in NuWro SF and $\mathrm{NuWro}+\mathrm{INCL}$ (comparison of the shapes between unit-normalized distributions). Bottom: $\delta {\alpha }_T$ distribution in NuWro SF and $\mathrm{NuWro}+\mathrm{INCL}$ (comparison of the shapes between unit-normalized distributions). The dashed line indicates the distribution obtained when the leading nuclear cluster is used as proton in INCL events. CCQE events with T2K neutrino energy flux are simulated.

Figure 11

Particles leaving the nucleus in events without a proton in the final state in INCL.

Figure 12

Total track length of nuclear clusters as a function of visible energy of the particles. The ${}^3\mathrm{He}$ distribution overlaps with the $\alpha$ distribution.

Figure 13

Momentum distribution of clusters produced by FSI in INCL (solid line) and visible energy loss by ionization (with the Birks correction) as a function of their momentum (scatter plot).

Figure 14

Visible energy deposited by ionization by different particles in a sphere of radius 3 cm around the vertex in events simulated with INCL.

Figure 15

Total visible energy deposited by ionization by all of the particles in a sphere of radius 1 (3) cm around the vertex. Distributions from events simulated with INCL and NuWro are compared with the same overall normalization.

Figure 16

Top to bottom: NuWro SF comparison to T2K data; $\mathrm{INCL}+\mathrm{NuWro}$ SF comparison to T2K data; comparison of NuWro, $\mathrm{INCL}+\mathrm{NuWro}$ SF and data; ratio of NuWro SF and $\mathrm{INCL}+\mathrm{NuWro}$ SF models of QE channel. Left: $\delta {\alpha }_T$; right: $\delta {\mathrm{p}}_T$.

Figure 17

Top to bottom: NuWro SF comparison to $\mathrm{MINER}\nu \mathrm{A}$ data; $\mathrm{INCL}+\mathrm{NuWro}$ SF comparison to $\mathrm{MINER}\nu \mathrm{A}$ data; comparison of NuWro, $\mathrm{INCL}+\mathrm{NuWro}$ SF and data; ratio of NuWro SF and $\mathrm{INCL}+\mathrm{NuWro}$ SF models of QE channel. Left: $\delta {\alpha }_T$, right: $\delta {\mathrm{p}}_T$.

Figure 18

Radial coordinate and momentum distribution inside the nucleus for NuWro RFG ($z$ axis in arbitrary units).

Figure 19

$\delta {\alpha }_T$ for NuWro RFG (left), $\mathrm{INCL}+\mathrm{NuWro}$ RFG (middle), and $\mathrm{INCL}+\mathrm{NuWro}$ RFG reweighted to INCL initial momentum and position (right).